Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • INDUSTRIAL PROCESSES STABILITY MODELING

      pg(s) 40-45

      A theoretical analysis of the stability of the non-equilibrium industrial processes is presented. A unified approach is proposed for the creation of the mathematical models of the processes that allows the determination of the velocities at which the processes move to their thermodynamic equilibriums and their use for mathematical analysis of processes velocities stability. For this purpose is used mathematical stability theory, evolution (autonomous) equations, bifurcation theory (stable focuses, stable cycles), parameter eigenvalues and eigenfunctions.

    • ABOUT NEW NONLINEAR PROPERTIES OF THE PROBLEM OF NONLINEAR THERMAL CONDUCTIVITY

      pg(s) 46-51

      In this paper we are consider a problem of nonlinear heat conduction with double nonlinearity under action of a strong absorption. For which an exact analytical solution is found, analysis of which makes it possible to reveal a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects are established: an inertial effect of a finite velocity of propagation of thermal disturbances, spatial heat localization and finite time effect i.e. existence of a thermal structure in a medium with strong absorption.

    • ENHANCED ASYNCHRONY IN THE VECTORIZED CONEFOLD ALGORITHM FOR FLUID DYNAMICS MODELLING

      pg(s) 52-54

      The application of a rigorous CFD method and an all-encompassing algorithmic performance optimization method can make possible the CFD simulation of the extremely large-scale problems, which allows simulation of either larger systems, or more detailed simulation of systems that are already simulated. The CFD code has to show both efficient one-node performance and excellent parallel scaling. The record breaking performance on one node has been achieved before with application of the LRnLA algorithm and making use of many core parallelism as well as the vectorization. In the current work, the algorithm is extended for many-node parallelism. The algorithms is characterized by high parallelization degree, small number of node communication events, and may be concisely described and programmed on the base of the previously implemented one-node solution, which is a rare feature among the algorithms with temporal blocking in all four of the spatial and time dimensions.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • STUDY OF STRESS-STRAIN STATE AND TEMPERATURE FIELD DURING ROLLING UNDER THE NEW SCHEME WITH ALTERNATING AND SHEAR DEFORMATIONS

      pg(s) 55-58

      In this paper, a computer simulation of a new technology of thick-sheet rolling, including rolling in rolls with a relief surface followed by rolling on rolls with a smooth barrel to the desired size. The analysis of effective plastic deformation, hydrostatic pressure and temperature field was carried out according to the results of modeling. According to the results of the analysis of effective strain, maximum of processing in the first pass receives the ridge area, but after the second pass observed alignment distribution of this parameter over the cross section. The study of the temperature field showed that the greatest temperature difference in the cross section occurs when rolling in relief rolls, in the future when rolling in smooth rolls due to the increase in the contact surface area, this difference decreases. Analysis of hydrostatic pressure showed the presence of both compressive and tensile stresses in the deformation zone. Such distribution is caused by the presence of a relief surface after 1 pass in the further alignment of the strip profile, which occurs both in the longitudinal and transverse directions.

    • MODELING AND SIMULATIONS OF AN UPPER LIMB EXOSKELETON DESIGNED FOR REHABILITATION AND TRAINING

      pg(s) 59-62

      The work presents a study of an upper limb exoskeleton designed for rehabilitation and training. While in the first stages of rehabilitation, when the patient is unable to move alone, the exoskeleton must be rigid, in the next stages it should be able to respond to any movement made by the patient. The key feature here is transparency: the robot must be able to “hide” if the patient is able to make the movement without assistance. The aim of the work is to identify and evaluate an appropriate solution of the upper limb exoskeleton that provides transparency and natural safety on the one hand, and force impact and performance on the other. In the paper, the mechanical model of the exoskeleton was shown. The mechanical structure is similar to the structure of the human arm. Through the kinematic model, the direct and inverse tasks of kinematics are solved using the Octave matrix software. The upper limb exoskeleton is designed as a haptic device that can perform tasks in virtual reality. Simulations of the interaction force between the patient and the exoskeleton were conducted also using the Octave software. Here, an assessment of the interaction force was made as a result of the exoskeleton passive impedance and the active control of the exoskeleton. Finally, conclusions and development recommendations are given.

    • MODELING OF TEMPERATURE DEPENDENCIES TO DETERMINE THE CONTENT OF SOLUBLE ELEMENTS IN THE BASIS OF DISPERSIONLY-HARDENING ALLOYS

      pg(s) 63-65

      The possibility of assessing of the temperature stability of the hardening phases of dispersion-hardened alloys with the help of polytherms of electrical resistance is experimentally confirmed. For alloys compositions of which belong to the quasi-binary Cu – Ni2Si cross section of the state diagram of the Cu – Ni – Si system, a procedure has been developed for calculating of the content of elements dissolved in the phase, based on copper, using data on temperature dependences of the electrical resistivity on temperature, presented in the form of regression equations. In the future, it is possible to use the developed model to assess the temperature stability of dispersed phases in alloys of more complex systems (for example, such as Cu – (Ni – Si) – (Fe – Cr – C)).

    • SIMULATION OF THE THERMAL STABILITY AND MELTING OF THE Ag@Pd, Au@Pd BIMETALLIC NANOPARTICLES

      pg(s) 66-69

      Within the framework of the molecular dynamics methods the simulation of the temperature stability of the metallic nanoparticles with the core-shell structure was performed and the melting temperature of the sample was determined. During the simulation of the dynamic behavior of nanoparticle the calculation of forces of interatomic interactions was carried out within the embedded atom method. To simulate the melting process the temperature of the sample was gradually increased by scaling the corresponding atomic velocities using the Berendsen thermostat. The Lindemann index was used as a numerical parameter describing changes in the structure of the nanoparticle. According to the results of the study, the temperature dependences of the Lindeman index and the average potential energy were obtained, as well as the radial distribution functions for the nanoparticles. From the simulation results, atomistic configurations of the sample were built and the dynamics of changes in its structure was investigated. Spatial distribution of the atoms on Lindeman index within the volume of the sample around melting temperature was also calculated.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • SECURITY THREAT PROPAGATION MODEL CIVIL AVIATION FACILITY

      pg(s) 70-72

      In the last few years there has outlined a well-defined tendency to consider aviation security with regard to the optimal management of its level with the consistent solution of the identification, measurement, evaluation and decision-making problems. For this purpose aviation security is shown as a state related to the object’s under study defined parameters, the quantitative display of which in the dynamics of their changes under the influence of external and internal factors remains in acceptable limits in terms of the object’s operation. However, the environment is formed by the object’s safety equipment, which represent a definite list of technical and other functional elements, solving the problem of the internal and external factors countermeasure. If we consider the situation of counter-strategy as a pseudo field, the proposed model belongs to the class of boundary value problems described by partial differential equations. The problem has no analytical solution, and computational modeling is very limited by mathematical formalization’s issues. It is offered to use hybrid computer tools, which have undoubted advantages in this case.